The first obertone of an open organ pipe beats with the first overtone of a closed organ pipe with a beat frequency of 2.2 Hz. The fudamental frequency of clos3ed organ pipe is 110 Hz. Find length of the open pipe. (Given, sound in air =330 m/s )

Options

A. 1.0067m only
B. 0.9937m only
C. 1.0067 or 0.9937m
D. 0.75m

Answer

C

Explanation

Let `l_c " and " l_0` represent the length of closed and open end organ pipes
`n_c=110 therefore n_1=3n_c=3xx110=330`
First overtone of closed pipe
`n_10 - n_(1c) = pm2.2`
`n_10-3n_c = pm 2.2`
gt `n_10-330 = pm 2.2`
`therefore n_10 = 322.2 " or " 327.8`
`l_(01) = (330)/(330pm2.2) = (330)/(332.2) " or " (330)/(327.8)`
` l_(01) = 0,9937 " or " 1.0067`